The bijectivity of mirror functors on tori

By the SYZ construction, a mirror pair (X,Xˇ) of complex torus X and partner Xˇ is described as special Lagrangian fibrations X→B Xˇ→B on same base space B. Then, by transform, we can construct simple projectively flat bundle from each affine multisection with unitary local system along it. However, there are ambiguities choices transition functions it, this causes difficulties when try to functor between symplectic geometric category category. In paper, prove that exists bijection set isomorphism classes their objects solving problem.